It is shown that there exist a continuous function f and a regulated function g defined on the interval [0,1] such that g vanishes everywhere except for a countable set, and the K *-integral of f with respect to g does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions.
In this paper a nonmonotone limited memory BFGS (NLBFGS) method is applied for approximately solving optimal control problems (OCPs) governed by one-dimensional parabolic partial differential equations. A discretized optimal control problem is obtained by using piecewise linear finite element and well-known backward Euler methods. Afterwards, regarding the implicit function theorem, the optimal control problem is transformed into an unconstrained nonlinear optimization problem (UNOP). Finally the obtained UNOP is solved by utilizing the NLBFGS method. In comparison to other existing methods, the NLBFGS method shows a significant improvement especially for nonlinear and ill-posed control problems.
In this paper we consider Neumann noncoercive hemivariational inequalities, focusing on nontrivial solutions. We use the critical point theory for locally Lipschitz functionals.
We investigate a relation about subadditivity of functions. Based on subadditivity of functions, we consider some conditions for continuous t-norms to act as the weakest t-norm TW-based addition. This work extends some results of Marková-Stupňanová [15], Mesiar [18].
In this paper, we give the mapping theorems on $\aleph $-spaces and $g$-metrizable spaces by means of some sequence-covering mappings, mssc-mappings and $\pi $-mappings.
In this paper, the relationships between metric spaces and $g$-metrizable spaces are established in terms of certain quotient mappings, which is an answer to Alexandroff’s problems.
In this note we study finite $p$-groups $G=AB$ admitting a factorization by an Abelian subgroup $A$ and a subgroup $B$. As a consequence of our results we prove that if $B$ contains an Abelian subgroup of index $p^{n-1}$ then $G$ has derived length at most $2n$.
In this note we give an answer to a problem of Gheorghiță Zbăganu that arose from the study of the properties of the moments of the iterates of the integrated tail operator.
We describe a class of bivariate copulas having a fixed diagonal section. The obtained class contains both the Fréchet upper and lower bounds and it allows to describe non-trivial tail dependence coefficients along both the diagonals of the unit square.